2019/12/13 by Sen Na, Mihai Anitescu, Na, Sen +1 · 2 citations
Computer Science · Economics, Econometrics and Finance · #Economic theories and models #FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1912.06734
openalex publication_date 2019/12/13 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper, we study the sensitivity of discrete-time dynamic programs\nwith nonlinear dynamics and objective to perturbations in the initial\nconditions and reference parameters. Under uniform controllability and\nboundedness assumptions for the problem data, we prove that the directional\nderivative of the optimal state and control at time k, boldsymbolx^*k\nand boldsymbolu^*k, with respect to the reference signal at time i,\n boldsymboldi, will have exponential decay in terms of |k-i| with a\ndecay rate \ρ independent of the temporal horizon length. The key technical\nstep is to prove that a version of the convexification approach proposed by\nVerschueren et al. can be applied to the KKT conditions and results in a convex\nquadratic program with uniformly bounded data. In turn, Riccati techniques can\nbe further employed to obtain the sensitivity result, borne from the\nobservation that the directional derivatives are solutions of quadratic\nprograms with structure similar to the KKT conditions themselves. We validate\nour findings with numerical experiments on a small nonlinear, nonconvex,\ndynamic program.\n